Do the Nile and Euphrates rivers originate in Paradise, and what is the evidence for that?

The previously mentioned hadiths regarding the Nile and the Euphrates are explicit in affirming that their origin is in Paradise. Al-Nawawi said: The origin of the Nile and the Euphrates is from Paradise, and they emerge from the base of the Lote Tree of the Utmost Boundary (Sidrat al-Muntaha), then flow as Allah wills, then descend to the earth, then flow therein, then emerge from it. This is not prevented by reason, and the apparent meaning of the narration has testified to it, so it should be relied upon. Ibn Hajar said: The gist is that their origin is in Paradise, and they first emerge from its source, then flow until they settle in the earth, then spring forth.